The Beauty Behind the Physics of Sound & Music

byCraigonSeptember 13, 2010

Intrinsic beauty in Music

My post, “Beauty In the Beast: What is beauty?”, identifies four unique ways in which we perceive beauty in the world, the arts, and specifically music. Those are Intrinsic, Associative, Learned, & Intellectual beauty. Just so you know, I coined those terms which may or may not coincide with terms that already exist. “Intrinsic Beauty” is a newer conversation and it excites me very much.

I was very excited to discover there are laws of physics in sound that align with and support my resolute belief in a traditional or, as some would say, old fashioned harmonic language for composition. There is no question that environmental and social influences (Associative and Learned) followed by the study of music (Intellectual) have and will likely always continue to determine what we perceive to be beautiful music. But the physics of sound and how our brains are hardwired to appreciate and understand it has been an interesting and much overlooked line of inquiry. Not anymore. It is a growing field of study. Perhaps the physics of sound has a lot more to do with what we perceive to be beautiful then we think or know – or perhaps we “know” without “thinking” about it.

Here’s what I have discovered so far:

Pitches, Frequencies and Noises

What do I mean when I say the “physics of sound”?

Almost all sounds we hear are actually a combination of many different pitches or frequencies. To be clear on terminology, an example of what we perceive to be a single pitch could be any single note played on a piano. Also, pitch and frequency are synonymous for the purposes of this conversation. Unpleasant sounds or noises are combinations of very many frequencies that are seemingly at war with each other. Also, often no one particular frequency predominates or comes into focus which results in overall effect which would often call a noise that we don’t like (like nails scraping on a black board). It is not harmonious to our ears.

Sounds which we instinctively know to be beautiful, like the melodious call of many song birds, are made up of a much more specific set of frequencies and it turns out the frequencies are mathematically related. These mathematical relationships explain why we perceive the sound as harmonious and melodic. When you hear a songbird sing a single note it may sound like you are hearing just one frequency, but actually, just as in the case of noise, you are hearing several frequencies all at once. The reason we hear the pitch as one pitch is that one single pitch is louder than all the others and we call this the fundamental frequency. The fundamental frequency is always the lowest sound of all the sounds we are hearing. It is so fundamental, that we are not consciously aware of the many other pitches we are also hearing at the same time. All these other frequencies that we are not aware of are called overtones. As I mentioned, they sound harmonious or pleasing to us as opposed to noise because there are clear mathematical relationships between the fundamental frequency and the overtones’ frequencies. For example, if we were to play the second lowest A note on a tuned piano, the frequency for that note happens to be 55 Hz. The first overtone above that is 110 Hz (2 x 55 Hz), exactly double the frequency of the fundamental 55 Hz pitch. The next overtone is 3 x 55 for 165 Hz, then 4 x 55 for 220 Hz, then 5 x 55 for 275 Hz and so on. So all the overtones have a clear numerical relationship to the fundamental pitch. Nature has created this and scientific studies have confirmed that our brains are hardwired to respond favorably to sounds that have these consonant sounding overtones.

Overtone List

Here is a list to show you the overtones and their relationships when a single A (55 Hz) note is played on the piano

Fundamental – 1 x 55 – 55 Herz – A

1st overtone – 2 x 55 – 110 Hz – A (1 octave higher)

2nd overtone – 3 x 55 – 165 Hz – E

3rd overtone – 4 x 55 – 220 Hz – A (2 octaves higher)

4th overtone – 5 x 55 – 275 Hz – C#

5th overtone – 6 x 55 – 330 Hz – E

6th overtone – 7 x 55 – 385 Hz – G

7th overtone – 8 x 55 – 440 Hz – A (3 octaves higher)

8th overtone – 9 x 55 – 495 Hz – B

9th overtone – 10 x 55 – 550 Hz – C#

10th overtone – 11 x 55 – 605 Hz – D

11th overtone – 12 x 55 – 660 Hz – E

12th overtone – 13 x 55 – 715 Hz – F#

13th overtone – 14 x 55 – 770 Hz – G

14 overtone – 15 x 55 – 825 Hz – G#

15th overtone – 16 x 55 – 880 Hz – A (4 octaves higher)

When that single A (55 Hz) is played on a piano you are actually hearing all those overtones. You do not notice them because they are much quieter than the fundamental, but they are all there and you are actually hearing them. There are pages and pages that can be written about overtones and many complexities about tuning I have intentionally ignored here (and am yet to understand myself), but I am intentionally keeping this inquiry simplified.

Notice the preponderance of A’s and E’s in the list of overtones. These pitches when played together on the piano create harmonies that are perceived by us as very consonant or easy to listen to. Also of note, is that these two notes (A and E) create two intervals called the perfect octave and the perfect 5th. These two intervals are foundational in the music of ALL known musical cultures. The human brain is designed to respond favorably to these intervals.

After that, the next most frequent pitch is C#. A, E, and C# just happen to create what we call a major triad. The major triad is foundational to Western Classical music up until the late 1800’s and to most of today’s popular music. Also to be found within the first 14 overtones are the notes that make up the major scale that the same music I just mentioned is primarily built on. It is no accident that we chose that scale – it is a natural part of the physics of sound. The overtone series is foundational to the scales of other cultures as well.

When we are born, our brains are already fully developed to appreciate the consonant sounds that exist in the overtone series. Our brains are not developed to understand and appreciate dissonant sounds or pitches that fall outside the normal bounds of the overtone series. In fact, a different region of our brain processes dissonant sounds. We develop a taste for dissonance as our brains develop and as we are repeatedly exposed to the music of our culture and society. For me, I love dissonance when it is followed by consonance. It is the tension and release of tension, the dance between less harmonious and very harmonious that I love and that moves me most profoundly. Study of music results in a much greater appreciation for dissonance and the ability to find beauty in it without the relief of consonance. I have had this experience. But, when the cards are down, I am ultimately left feeling unsatisfied and incomplete if the consonant sounds as nature appears to have designed them do not reappear. There comes a point when too much dissonance becomes uninteresting and almost flat sounding. I love the dance between the two poles, like Ying and Yang. It is the dance between consonance and dissonance that is ultimately most interesting and perhaps even most beautiful to me.

Some 20th and 21st Century masters of dissonance and consonance that leap to mind are: